Quasimonotone Multifunctions; Applications to Optimality Conditions in Quasiconvex Programming
A. Hassouni · Numerical Functional Analysis and Optimization · 1992
In this paper we introduce a concept of quasimonotonicity for multifunctions defined on a space X with values in X ∗, the dual of X, and give some properties of this class of multifunctions. By using the fact that, for generalized gradients of locally lipschitz functions, quasimonotonicity gives an extremely useful characterization of quasiconvexity, we show some properties of the normal cone to the level set of f. We then obtain necessary and sufficient optimality conditions in quasiconvex programming via some variational inequalities.